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1. math.stackexchange.com › questions › 1024280Most ambiguous and inconsistent phrases and notations in maths

   math.stackexchange.com › questions › 1024280

   Nov 18, 2014 · What are some examples of notations and words in maths which have been overused or abused to the point of them being almost completely ambiguous when presented in new contexts? For instance, a function $f$: $f^{-1}(x)$ can be an inverse and a preimage and sometimes even $\frac{1}{f(x)}$. $f^2(x)$ can be $(f\circ f)(x)$ and $(f(x))^2$.

2. people.math.harvard.edu › ambiguity › ambiguityAMBIGUOUS PEMDAS - Harvard University

   people.math.harvard.edu › ambiguity › ambiguity

   AMBIGUOUS PEMDAS. OLIVER KNILL. Abstract. A source collection about the mathematical syntax in the ring Z. 1. Pemdas. 1.1. In the commutative additive group (Z; +; 0) one usually writes x for the inverse element. One has then x + ( x) = 0 or x x = 0 for short.

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3. www.people.vcu.edu › ~rhammack › Math490Mathematical Writing - Virginia Commonwealth University

   www.people.vcu.edu › ~rhammack › Math490

   Since x and X can have entirely di erent meanings, putting such symbols at the beginning of a sentence can lead to ambiguity. Following are some examples of bad usage (marked with ) and p good usage (marked with ). is a subset of B. The set A is a subset of B. is an integer, so 2x + 5 is an integer. Since x is an integer, 2x + 5 is an integer.

4. davidwees.com › ambiguity-mathematical-notationAmbiguity in mathematical notation – The Reflective Educator

   davidwees.com › ambiguity-mathematical-notation

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   Jul 9, 2013 · Off the top of my head, two examples of notation that often confuse some students: Inverse trig function notation sin^(-1)(x)≠(sin x)^(-1) even though sin^2(x)=(sin x)^2. Function notation in general: sin(x) confused with “sin” times “x”

5. nrich.maths.org › articles › numbers-and-notationNumbers and Notation - Ambiguities and Confusions - NRICH

   nrich.maths.org › articles › numbers-and-notation

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   Some occur only in rather specialised situations, but many are fundamental and part of everyday experience. Here are some items from my collection - reactions and further examples will be appreciated.

6. www.columbia.edu › ~is375 › Mathematical NotationCommonly Used Mathematical Notation - Columbia University

   www.columbia.edu › ~is375 › Mathematical Notation

   Some examples of common set notation: f; g set brackets: the set of ... e.g. fa; b; cg means the set consisting of a, b, and c. fjg set builder notation: the set of ... such that ... i. fxjP(x)g means the set of all x for which P(x) is true.

7. People also ask

   What are some examples of ambiguous notations and words in maths?

   • What are some examples of notations and words in maths which have been overused or abused to the point of them being almost completely ambiguous when presented in new contexts? For instance, a function f: f − 1(x) can be an inverse and a preimage and sometimes even 1 f (x). f2(x) can be (f ∘ f)(x) and (f(x))2.

   Most ambiguous and inconsistent phrases and notations in maths

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   What is an example of an ambiguity from MSE?

   • In other words, if A ⊂ B and B ⊂ A then A = B rather than a contradiction. Here is an example of an ambiguity from MSE: Proof verification: prove A ⊆ B if and only if A ∩ B = A. "X is dense in itself" is not equivalent to "X is dense in X". An ellipse is not an elliptical curve.

   Most ambiguous and inconsistent phrases and notations in maths

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   Is the word 'non-trivial' ambiguous?

   • Note that the converse, of course, is the word "non-trivial," which is just as ambiguous. I'll also note that although you may consider this a trivial answer, but I have had students get tripped up by my usage of the word "trivial" in lecture, so the ambiguity must be somewhat non-trivial. I feel like your answer needs a little more justification.

   Most ambiguous and inconsistent phrases and notations in maths

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   Is abuse of notation a reason?

   • @MarianoSuárez-Alvarez: I don't follow your reasoning. Every widely-used abuse of notation happens for a reason; just because there's a reason or context behind it doesn't mean it's not an abuse of notation.

   Most ambiguous and inconsistent phrases and notations in maths

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   Is sin 1x an abuse of notation?

   • Also: sin − 1x is definitely an abuse of notation. It is not the inverse function, but refers to the inverse of a specific restriction of sinx to a domain on which it's injective. Note that cos − 1 and tan − 1 are also used, and their restrictions are different. This notation can only be defined in an extremely kludgy way.

   Most ambiguous and inconsistent phrases and notations in maths

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   Why is XDx = x2 2 ambiguous?

   • Even ignoring the problem in 1., the symbol ∫ xdx = x2 2 is ambiguous as it can mean a number of things. Under one of the common interpretations the equal sign doesn't even denote an equality. I allude to that meaning here, (it is the same issue as with f = O(g)).

   Most ambiguous and inconsistent phrases and notations in maths

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8. www.researchgate.net › publication › 270903183(PDF) Polysemy of symbols: Signs of ambiguity - ResearchGate

   www.researchgate.net › publication › 270903183

   Jul 1, 2010 · article focused on particular examples of distinguishing among the symbolic notation for arithmetic over the set of natural numbers, rational numbers, equivalence classes, and transfinite